Quantum Dynamics of a Hyper-Raman Coupled Model Interacting with Two Quantized Cavity Fields

The quantum dynamics of a hyper-Raman coupled model interacting with two modes of the quantized cavity field is described. The model consists of a four-level atom in a v configuration where transitions between the ground and excited states occur through the absorption (emission) of two photons from one mode and the emission (absorption) of one photon from the other and where two intermediate states are taken to be far off-resonance and are adiabatically removed. This is a multiphoton extension of the Jaynes-Cummings model and is exactly solvable. We study the atomic inversion and investigate the production of non-classical light exhibiting antibunching, violations of the Cauchy-Schwartz inequality, and squeezing.     

Quantum Nonlinear Sigma Model with a Damping Term; Finite Temperature Renormalization Group Analysis

We study the behavior of the finite temperature quantum nonlinear sigma model in two dimensions in the presence of the damping of the form f (|w_n|) = g|w_n|^af (|\omega_n|) = \gamma |\omega_n|^\alpha, where α satisfies a 3 1\alpha \ge 1. The analytical calculations will be performed using a = 2\alpha = 2 and the results will be compared with the standard results obtained for the standard quantum nonlinear sigma model. The behavior of such a system is connected with the pseudogap which appears in the normal state of the cuprate superconductors.     

Quantum Nonlinear Sigma Model with a Damping Term; Finite Temperature Renormalization Group Analysis

We study the behavior of the finite temperature quantum nonlinear sigma model in two dimensions in the presence of the damping of the formf (|θ _n |) = γ|ω _n |^α, whereα satisfiesα ≥ 1. The analytical calculations will be performed usingα=2 and the results will be compared with the standard results obtained for the standard quantum nonlinear sigma model. The behavior of such a system is connected with the pseudogap which appears in the normal state of the cuprate superconductors.     

Propagation of Short Light Pulses in Nonlinear Birefringent Fibre

Abstract

An analytical approach is developed to obtain the solution of coupled Schrödinger equations for polarization components of a solitary wave. Variational analysis allows us to describe optical pulse propagation in fibres with nonlinear birefringence. Conditions for polarization channel switching and locking are formulated.     

One-Dimensional Quantum Compass Model in an Out-plane Magnetic Field

The one-dimensional quantum compass model (1D-QCM) in an out-plane magnetic field is investigated by numerical and analytical methods. The presence of the 1D-QCM in an area of the ground-state magnetic phase diagram where the odd couplings are antiferromagnetic and larger than the even couplings is studied. Using pseudo spin ladder operators indicates that the 1D-QCM in an out-plane magnetic field can be mapped to the one-dimensional Ising model in a transverse magnetic field (ITF). Analytical investigation of the effective ITF Hamiltonian predicts the occurrence of two quantum phase transitions with increasing magnetic field. Also, the critical fields are obtained from this method, which are completely in agreement with the results of the numerical experiment based on the Lanczos method. This numerical method accurately determined the behavior of the energy gap, magnetization and string order parameter, and therefore it is a very useful method for indicating the ground-state phases of the system.     

Nonlinear Dynamics of Frontal Polymerization with Autoacceleration

A free-boundary model is used to describe frontal polymerization. Autoacceleration effects, such as the gel effect, are accounted for in the formulation. Weakly nonlinear analysis is applied to investigate pulsating instabilities in two dimensions. The analysis produces a pair of Landau equations that describe the evolution of the linearly unstable modes. Autoacceleration influences the linear stability of the system as well as the onset and stability of spinning and standing modes.     

Investigation of the Neutron Quantum States in the Earth’s Gravitational Field

We studied the neutron quantum states in the potential well formed by the Earth’s gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in two lowest quantum states correspond to their expectations with an accuracy of ≈25 %. The spatial density distribution in a standing neutron wave above a mirror was measured for a set of a few lowest quantum states. A position-sensitive neutron detector with an extra high spatial resolution of 1 μm to 2 μm was developed and tested for this particular task. Although this experiment was not designed or optimized to search for an additional short-range force, nevertheless it allowed us to slightly improve the published boundary in the nanometer range of characteristic distances. We studied systematical uncertainties in the chosen “flow-through” method as well as the feasibility to improve further the accuracy in this experiment.     

Nonlinear Dissipative Oscillator with Displaced Number States

Abstract

We study the interaction of a Kerr-like medium with light initially prepared in a displaced number state. We analyse squeezing properties and photon statistics at the output of a Kerr-like medium. We show that under certain conditions the superposition of two displaced number states can be created. We study the influence of dissipation on the formation of the superposition state.     

Quantum Statistical Properties of Coupled Nonlinear Oscillators with Losses

Abstract

The statistical properties of two coupled nonlinear oscillators including losses are discussed using the statistics for the generalized superposition of coherent fields and quantum noise. Exact and approximate formulae for squeezing of vacuum fluctuations are derived. The photon statistics are shown to be Poissonian from the nonlinear dynamics of the lossless case. Non-classical behaviour is degraded by noise.     

Dynamics of a Q-analogue of the Quantum Harmonic Oscillator

Abstract

We analyse the dynamics of the q-deformed quantum harmonic oscillator initially prepared in the q-analogue of the coherent state. Non-trivial behaviour of the mean values of the q-position operator is observed. The squeezing of the second-order moments of this operator is studied.     

Measure of Entanglement States of Two Interacting Electrons in Vertically Coupled Quantum Dots Induced by a Time-Dependent Electric Field

We study the dynamics of two electrons located in two vertically tunnel-coupled quantum dots in the presence of an oscillatory electric field. By solving the time-dependent Schrödinger equation, we predict the dynamical generation of entangled electron states, such as the EPR (Einstein, Podolsky, and Rosen) pairs or Bell states. The Schmidt rank and the von Neumann entropy are evaluated to characterize the degree of entanglement of the two electron states.     

量子引力场中纳米颗粒的量子理论

首次给出纳米颗粒哈密顿量的明确表示。根据纳米颗粒的量子自旋特性,得到纳米颗粒质量随时间变化的规律。根据纳米颗粒哈密顿量的守恒条件,得到纳米颗粒的量子平动动量、纳米颗粒的量子转动动量、纳米颗粒所受的量子引力及纳米颗粒与纳米颗粒引力中心的量子距离随时间变化的规律。证明纳米颗粒的量子平动动量、纳米颗粒与纳米颗粒引力中心的量子距离、纳米颗粒的量子能量均与颗粒所处的量子状态有关。对于不同量子状态的纳米颗粒,上述物理量的取值不同。本文中创新一组满足对易关系互为共轭的复量子数算符,建立纳米颗粒的量子算符代数理论,得到纳米颗粒能量的量子化表示。     

Effect of Dzyaloshinskii-Moriya Interaction on Thermal Quantum Correlation in a Two-Qubit Heisenberg XXZ Model with an Inhomogeneous External Magnetic Field

By using the two-qubit Heisenberg XXZ model with Dzyaloshinskii-Moriya (DM) interaction and an inhomogeneous external magnetic field, we investigate the similarities and differences of negativity (N), quantum discord (QD), and measurement-induced disturbance (MID) and the behaviors of quantum phase transition (QPT) at finite temperature. The results indicate that DM interaction D can enhance the N, QD, and MID, while the uniform magnetic field B suppresses them, and the role played by the inhomogeneity b of magnetic field in N is obviously different from those in QD and MID for the smaller D region. Moreover, compared with N, we notice the QD and MID are more general measures of the thermal quantum correlation (TQC). And that the MID cannot completely replace the QD has been discovered. It is also observed that the DM interaction is a more optimal parameter than the inhomogeneous external magnetic field in the process of improving the TQC measured by QD and MID at the higher temperature. In addition, we note that the DM interaction and an inhomogeneous external magnetic field present remarkable different effects on the behavior of the QPT point at finite temperature.     

非线性转子动力学研究综述

综述了国内外非线性转子动力学的研究现状,讨论了非线性转子动力学研究中的7个主要问题,并引述了大量相应的国内外文献,包括：非线性转子动力学研究的一般方法;求解非线性转子动力学问题的数值积分方法;大型转子－轴承系统高维非线性动力学问题的降维求解;基于微分流形的动力系统理论方法;转子非线性动力学行为的机理研究和实验研究;高速转子－轴承系统的非线性动力学设计,最后讨论了非线性转子动力学研究中存在的问题及展望。     

一类驰振问题的非线性动力学研究

研究半圆柱体模型在气动载荷作用下的非线性动力学行为.利用计算流体力学软件FLUENT和符号代数软件Mathematica对系统进行分析.利用平均法对系统进行了近似求解, 得到了系统的运动相图及时间历程曲线,结果表明系统运动收敛于稳定的极限环,所得结果与实验吻合得较好.提出了一种综合运用Fluent软件和非线性动力学理论研究驰振问题的方法.     

Binary Optical Communication with Quantum Signals Propagating in Nonlinear Media

Abstract

Quantum signals propagating in nonlinear media are studied with the anharmonic oscillator model. The results are used to calculate the information and the signal-to-noise ratio in binary optical communications which use those signals.     

Field Dependent Effects in a Quadratic Nonlinear Medium

Field-dependent phase shift and conversion efficiency of parametric processes in quadratic lossless nonlinear media are studied as a function of phase mismatch and of input field amplitude.     

Logistic增长的时滞SIS模型分析

本文研究了一类具有生理阶段结构的Logistic增长的SIS传染病模型,给出了系统边界平衡点和正平衡点全局渐近稳定的条件。即得到了传染病最终消除和成为地方病的阈值。